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A collection of 36 cards consists of 4 sets of 9 cards each.

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A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink] New post 07 Jan 2014, 04:13
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.

Data Sufficiency
Question: 21
Category: Arithmetic Properties of numbers
Page: 154
Difficulty: 600


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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink] New post 07 Jan 2014, 04:14
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A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one cadrd has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6 --> we can get the sum of all 36 cards: sum=4(1+2+3+4+5+6+7+8+9) --> thus we can get which card should be removed so that the new sum to have the units digit of 6 (as cards are from 1 to 9). Sufficient.

(2) The sum of the numbers on the remaining 35 cards is 176 --> the same here. Sufficient.

Answer: D.
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink] New post 07 Jan 2014, 08:08
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Total sum of numbers on 4 decks is [(9X10)/2]X4=180

1. only 180- 4 will be get you a units digit of 6. Hence 4 is the withdrawn card. --> Sufficient
2. 180 -4 =176 . Hence again 4 is the withdrawn card. --> Sufficient

Hence D
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink] New post 07 Jan 2014, 23:03
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45 is the sum of each set (n(n+1)/2, n=9).Thus total sum would be 45*4 = 180.

Statement 1: subtracting x (x<=9) from 180 should give a units digit of 6, i.e. x=4 ---> Sufficient
Statement 2 : sum of remaining cards: 176, only 4 is left out. Sufficient

So D it is :) :)
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink] New post 08 Jan 2014, 07:57
Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

A collection of 36 cards consists of 4 sets of 9 cards each. The 9 cards in each set are numbered 1 through 9. If one card has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6.
(2) The sum of the numbers on the remaining 35 cards is 176.



The value of the card can be 1 to 9.
Statement 1) Sum of all the cards of one set = 1+2+..+9 = 9*10/2 = 45
So all the 4 sets = 4*45 = 180
last digit is 6 so card has to have a value of 4 because no other card number will satisfy the condition.

Statement 2) The sum is even more explicit. So definitely we can determine.

Hence option D)
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Re: A collection of 36 cards consists of 4 sets of 9 cards each. [#permalink] New post 11 Jan 2014, 06:10
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SOLUTION

A collection of 36 cards consists of 4 sets of 9 cards in each set are numbered 1 through 9. If one cadrd has been removed from the collection, what is the number on that card?

(1) The units digit of the sum of the numbers on the remaining 35 cards is 6 --> we can get the sum of all 36 cards: sum=4(1+2+3+4+5+6+7+8+9) --> thus we can get which card should be removed so that the new sum to have the units digit of 6 (as cards are from 1 to 9). Sufficient.

(2) The sum of the numbers on the remaining 35 cards is 176 --> the same here. Sufficient.

Answer: D.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A collection of 36 cards consists of 4 sets of 9 cards each.   [#permalink] 11 Jan 2014, 06:10
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